Dame Maggie Smith’s trophy cabinet reflected her extraordinary achievements across theatre, film and television – and in the biggest arenas of British and US culture, from the BBC to Hollywood, the West End to Broadway. A measure of her versatility and durability is that, in the 1960s, she played nine major roles in the formative years of the National Theatre, but also, from the start of the 2000s, appeared in five series of Downton Abbey, the ITV Sunday night series that became one of the biggest popular hits of the new millennium.

Her role in that show was Violet Crawley, Dowager Countess of Grantham, who lived in such a bubble of exclusive comfort that, in trademark one-liners, she would drawl in mystification, for example: “What is a ‘weekend’?” That acerbic superiority was a signature throughout Smith’s career, including the part that brought her first Academy award in 1970, against a shortlist also featuring Liza Minnelli and Jane Fonda, for the title role in The Prime of Miss Jean Brodie, adapted from Muriel Spark’s novel about a maverick, arrogant schoolteacher in Edinburgh.

Smith consistently had the courage and talent to do unexpected things. Her second Oscar, in 1979, was for California Suite, with a script by Neil Simon and a cast of high Hollywood talent including Alan Alda and Walter Matthau. Introducing an element of postmodernism to a mainstream comedy, Smith played exactly what she had been at the start of the decade: an English actress up for her first Academy award.

Another surprise on her CV demonstrated an ability to play it straight and dark. In 2019, after 12 years away from the stage, Smith, at the age of 84, performed a 100-minute monologue at the Bridge theatre in London. A German Life was adapted by Christopher Hampton from a documentary movie interview given, at the age of 102 (the show was a rare case of an octogenarian ageing up for a part), by Brunhilde Pomsel, who worked for the Nazi propaganda chief Joseph Goebbels during the Holocaust, but who continued to deny complicity or guilt. With typical meticulousness, Smith refused to accept the part until she had proved to herself at home that she could memorise an extended solo. Combining enduringly impeccable technique with the guts to test it again at such an age, it was a late triumph in an astonishing career.

Margaret Smith – she preferred her full first name, the “Maggie” imposed on her to distinguish from another performer on the Equity register – was born in Ilford, Essex. Her mother, who worked as a secretary, was Scottish, so useful for the creation of the Brodie brogue. Her father, Nathaniel, was a pathologist, whose academic posting to Oxford led to his daughter attending the city’s girls’ high school.

Despite joining the Oxford Playhouse Company at 16, rather than going to college, Smith benefited from the local varsity theatrical privileges, cast in Oxford University Dramatic Society productions, including revues, which, at the time were attended by national critics.

Such was the impact she made in comedy skits and songs that, aged 21, she was part of an ensemble recruited to appear on Broadway in a revue called New Faces of 1956. In London, during the following two years, she appeared, with co-stars including Kenneth Williams, in an English show, Share My Lettuce, billed as “a diversion with music”, with a script by Bamber Gascoigne.

At that point, Smith seemed set to be a sketch-and-music comedian, especially when Strip the Willow, a play about the survivors of a nuclear war in the UK, failed to transfer to London from a UK tour. It was written by Beverley Cross, whom Smith had met at the Oxford Playhouse. He wrote the play for her as an attempted seduction, the first description of her character being “beautiful. As elegant and sophisticated as a top international model. A great sense of fun. A marvellous girl.’’

However, at that stage, no lasting relationship occurred. And Smith’s serious dramatic career was launched when she appeared, again paired with Kenneth Williams, in a double bill of plays, The Private Ear and The Public Eye, by Peter Shaffer, in 1962. These won Smith her first Evening Standard best actress statuette, at the age of 27, and caught the attention of Sir Laurence Olivier, then establishing, at Chichester, the first attempt at a National Theatre. Crucially to the development of her reputation, Olivier trusted her not only with comedy – such as The Recruiting Officer, George Farquhar’s early 18th-century farce – but also tragedy: she was Desdemona to Olivier’s performance in the title role of Othello.

Also at the National, Smith formed a relationship with the actor Robert Stephens, who became her first husband, and father of her sons, who, as Toby Stephens and Chris Larkin, followed their parents into acting.

Dramatic Exchanges, a collection of correspondence from the National Theatre archives, shows the close creative relationship between Olivier and Smith. A habitual nicknamer, he addressed her as “Mageen”. He had long told her that her perfect role would be Millamant, a strong-willed woman conspiring to achieve a desired marriage, in William Congreve’s Restoration comedy The Way of the World. But, in 1968, with Smith having left the company following her marriage with Stephens and pregnant with their first child, Olivier proceeded to stage the play with Geraldine McEwan as Millamant.

Olivier’s letter of apology to Smith contained elaborately verbose admiration. Smith wrote a reply of pained regret concluding: “Well, what’s the point of trying to tell you my feelings. They obviously count for so very little. It was nice of you to say you will devote your energies to my return but really I do not think it would be wise of me to believe that either. Margaret.”

There is a waspish, unforgiving tone in that letter that was part of Smith’s personality; some of those who worked with her, especially younger actors struggling with their roles, were wounded by witty but cruel putdowns.

That bad casting luck at the National, though, was more than balanced out. Had Julie Andrews, in the same year, not turned down the Jean Brodie movie, Smith would never have played the part that redefined her career. With her American bankability increased by a US tour of Noël Coward’s Private Lives, Smith used it to go into a kind of theatrical exile from Olivier and Britain. From 1976 to 1980, she played four summer seasons at the Shakespeare festival in Stratford, Ontario, conceived as a sort of ex-pat RSC-National, where she finally played the part of Millamant and other roles that might have been expected in London, such as Lady Macbeth.

Smith fell into a happy rhythm of filming gigs split with Canadian acting sabbaticals. While she rehearsed or acted, Beverley Cross wrote to her, having become Smith’s second husband in 1975 following her divorce from Robert Stephens.

When Smith returned to London theatre, she took over from Diana Rigg as the troubled modern colonial wife Ruth Carson, in Tom Stoppard’s Night and Day. She confirmed her resurgence with two more Evening Standard awards, in 1981 and 1984, for London runs of shows she had premiered in Canada. In Virginia, by Edna O’Brien, she was the writer Virginia Woolf, for whom Smith’s gift for haughty wit made her natural casting. Then, 16 years after the disappointment with Olivier, she finally played the coveted role in The Way of the World in her own city.

Smith, in contradiction of the standard professional graphs, had, after that slight mid-career dip, a third act even more glorious than her first. Shaffer wrote for her Lettice and Lovage, a comedy maximising her command of sardonic superiority, as Lettice Douffet, a tour guide who begins to embellish history. She took the play to New York, where she won a Tony award. Smith also became an Alan Bennett specialist. She co-starred with Michael Palin in the movie A Private Function in 1984, as a Yorkshire woman using a black-market pig to prevent wartime rationing thwarting her upward mobility. In the 1988 first series of Bennett’s Talking Heads monologues for television, she was a vicar’s wife, anxious about private sins, in A Bed Among the Lentils. On stage (1999) and screen (2015), she was memorable as The Lady in the Van, a fictionalised version of Miss Shepherd, a Catholic evangelist tramp who for some years lived in a caravan on Bennett’s driveway.

There was a trio of West End appearances in plays by the great American dramatist Edward Albee: as the oldest (90-something) of three versions of the writer’s imperious mother in Three Tall Women (1994); playing a vicious drunk in a family menaced by an unnamed “plague” in A Delicate Balance (1997); and a mysterious matriarch visiting a deathbed in The Lady from Dubuque (2007), a rare flop that put Smith off theatre.

Another reason for her retreat from theatre was, unusually for a septuagenarian performer, a vast demand from movie studios. Between 2001 and 2011, she appeared in seven of the eight Harry Potter films, as Professor Minerva McGonagall, transfiguration teacher at Hogwarts, her embodiment of the formidable Scottish academic seeming to contain affectionate nods to Brodie. The part brought Smith considerable wealth – she joked about the “Harry Potter pension fund” – and a vast new fanbase that, she complained, made it impossible for her to shop in Waitrose any more.

Her cinematic renaissance had also included Robert Altman’s Gosford Park (2001). In this English country house drama, written by Julian Fellowes, Smith’s character was at least a first cousin to her Downton Abbey countess. Appearing in a TV series with an average audience of 10 million made it even harder for Dame Maggie (as she had become in 1990) to go shopping. But this late superstardom, half a century or more after her first major theatre and movie successes, confirmed that she was an actor with the rare ability to do anything she wanted anywhere.

• This article was amended on 27 September 2024. Brunhilde Pomsel was not Jewish as an earlier version had mistakenly said.